负刚度研究综述

Review of Research on Negative Stiffness

摘要: 负刚度是一种特殊的等效刚度特性，其主要表现为结构在某一工作区间内外力与位移增量方向相反。与传统正刚度系统相比，负刚度单元本身通常不能单独稳定工作，但当其与正刚度、阻尼或惯性元件合理组合后，可以显著降低系统等效动态刚度，从而改善低频隔振和减振性能。近年来，负刚度结构在准零刚度隔振、精密仪器隔振、航天器微振动控制、车辆与船舶振动控制、建筑结构减振以及机械超材料等领域受到广泛关注。本文围绕负刚度的基本概念、物理实现原理、动力学挑战、工程应用和发展趋势进行综述。首先阐明负刚度与准零刚度、高静刚度低动刚度之间的关系；然后按照负刚度形成的物理机制，将典型实现方式归纳为几何非线性型、失稳型、势能重构与多稳态型、场力型以及结构单元与机械超材料型；接着将低频隔振、稳定性、非线性频响、参数敏感性和阻尼耦合等内容整合为“负刚度系统的动力学挑战与关键科学问题”，重点讨论稳定工作区间、跳跃与分岔、多参数匹配和安全边界识别；最后总结当前研究中存在的参数调节能力不足、工程验证不充分和可靠性评价体系不完善等问题，并对可调负刚度、多向隔振、智能材料耦合和真实工况试验研究进行展望。综述表明，负刚度技术为低频振动控制提供了有效思路，但其工程应用仍需要在稳定性设计、参数优化和试验验证方面进一步完善。

Abstract: Negative stiffness is a unique equivalent stiffness property characterized by an opposite incremental relationship between force and displacement within a specific operating range. Compared with traditional positive-stiffness systems, negative-stiffness elements usually cannot work stably on their own; however, when they are properly combined with positive-stiffness, damping, or inertial elements, the equivalent dynamic stiffness of the system can be significantly reduced, thereby improving low-frequency vibration isolation and vibration mitigation performance. In recent years, negative-stiffness structures have attracted increasing attention in quasi-zero-stiffness vibration isolation, precision instrument isolation, spacecraft micro-vibration control, vehicle and ship vibration control, civil structural vibration reduction, and mechanical metamaterials. This review discusses the basic concepts, physical implementation principles, dynamic challenges, engineering applications, and development trends of negative stiffness. First, the relationship among negative stiffness, quasi-zero stiffness, and high-static-low-dynamic stiffness is clarified. Then, typical implementations are reorganized according to their physical mechanisms, including geometric-nonlinearity type, instability type, potential-energy-reconfiguration and multistable type, field-force type, and structural-unit/metamaterial type. Subsequently, the contents related to low-frequency isolation, stability, nonlinear frequency response, parameter sensitivity, and damping coupling are integrated into an independent section entitled “dynamic challenges and key scientific issues of negative-stiffness systems”. The discussion focuses on stable operating ranges, jump and bifurcation phenomena, multi-parameter matching, and identification of safe operating boundaries. Finally, current issues such as insufficient parameter adjustability, inadequate engineering verification, and incomplete reliability assessment are summarized, and future directions, including adjustable negative stiffness, multi-directional isolation, intelligent-material coupling, and tests under realistic operating conditions, are discussed. The review indicates that negative-stiffness technology provides an effective approach for low-frequency vibration control, but further work is still required in stability design, parameter optimization, and experimental validation before broader engineering application.